Difference in Proportions Hypothesis Test
A Difference in Proportions Hypothesis Test is a statistical hypothesis test based on comparing whether population proportions have an equal statistic.
- Context:
- It can range from being a Left-Tailed Difference in Proportions Test, to being a [[]] to being a [[]].
- …
- Example(s):
- a Difference in Means Test.
- “A telephone poll of 800 randomly selected people asked 'Should the federal tax on cigarettes be raised to pay for health care reform?'. Given the results, is there sufficient evidence at the α = 0.05 level to conclude that the smokers and non-smokers populations differ significantly with respect to their opinions?”
- Counter-Example(s):
- See: Statistical Test, Chi-Square Test, ANOVA, Z-Value.
References
2014
- https://onlinecourses.science.psu.edu/stat414/node/268
- QUOTE: So far, all of our examples involved testing whether a single population proportion p equals some value p0. Now, let's turn our attention for a bit to testing whether one population proportion p1 equals a second population proportion p2. Additionally, most of our examples thus far have involved left tailed tests in which the alternative hypothesis involved [math]\displaystyle{ H_A: p \lt p_0 }[/math] or right tailed tests in which the alternative hypothesis involved [math]\displaystyle{ H_A: p \gt p_0 }[/math]. Here, let's consider an example that tests the equality of two proportions against the alternative that they are not equal. Using statistical notation, we'll test [math]\displaystyle{ H_0: p_1 = p_2 }[/math] versus [math]\displaystyle{ HA: p_1 ≠ p_2 }[/math] …
The test statistic for testing the difference in two population proportions, that is, for testing the null hypothesis [math]\displaystyle{ H_0: p_1−p_2=0 }[/math] is: [math]\displaystyle{ Z=\frac{(\hat{p}_1−\hat{p}_2)−0}{\sqrt{\hat{p}(1−\hat{p})(\frac{1}{n_1}+\frac{1}{n_2})}} }[/math] where: [math]\displaystyle{ \hat{p}=\frac{Y1+Y2}{n1+n2} }[/math] the proportion of "successes" in the two samples combined.
- QUOTE: So far, all of our examples involved testing whether a single population proportion p equals some value p0. Now, let's turn our attention for a bit to testing whether one population proportion p1 equals a second population proportion p2. Additionally, most of our examples thus far have involved left tailed tests in which the alternative hypothesis involved [math]\displaystyle{ H_A: p \lt p_0 }[/math] or right tailed tests in which the alternative hypothesis involved [math]\displaystyle{ H_A: p \gt p_0 }[/math]. Here, let's consider an example that tests the equality of two proportions against the alternative that they are not equal. Using statistical notation, we'll test [math]\displaystyle{ H_0: p_1 = p_2 }[/math] versus [math]\displaystyle{ HA: p_1 ≠ p_2 }[/math] …
2012
- http://stattrek.com/hypothesis-test/difference-in-proportions.aspx
- QUOTE: Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The table below shows three sets of hypotheses. Each makes a statement about the difference d between two population proportions, P1 and P2. (In the table, the symbol ≠ means " not equal to ".)
The first set of hypotheses (Set 1) is an example of a two-tailed test, since an extreme value on either side of the sampling distribution would cause a researcher to reject the null hypothesis. The other two sets of hypotheses (Sets 2 and 3) are one-tailed tests, since an extreme value on only one side of the sampling distribution would cause a researcher to reject the null hypothesis.
- QUOTE: Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The table below shows three sets of hypotheses. Each makes a statement about the difference d between two population proportions, P1 and P2. (In the table, the symbol ≠ means " not equal to ".)
Set Null hypothesis Alternative hypothesis Number of tails 1 P1 - P2 = 0 P1 - P2 ≠ 0 2 2 P1 - P2 > 0 P1 - P2 < 0 1 3 P1 - P2 < 0 P1 - P2 > 0 1